How to Find GCF of 1657/584, 6870/824?

GCF of 1657/584, 6870/824

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 1657/584, 6870/824 i.e 1/60152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1657/584, 6870/824.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 1657/584,6870/824?

Given fractions are 1657/584,6870/824

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 1657/584,6870/824, numerators are 1657,6870

Denominators are 584,824

The GCF of 1657,6870 is 1 .

LCM of 584,824 is 60152.

The greatest common factor of 1657/584,6870/824 = [GCF of 1657,6870]/[LCM of 584,824]= 1/60152

Therefore, the GCF of 1657/584,6870/824 is 1/60152.

Greatest Common Factor of 1657,6870

To find the highest common factor of 1657,6870, we have to find the factors of both numbers and list the highest common factor.

The factors of 1657 are 1, 1657

The factors of 6870 are 1, 2, 3, 5, 6, 10, 15, 30, 229, 458, 687, 1145, 1374, 2290, 3435, 6870

The HCF of 1657,6870 is 1.

Lets's calculate GCF of 1657,6870

Greatest Common Factor (GCF) of 1657,6870 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 1657,6870 By Matching Biggest Common Factor Method

Now, list down the factors of 1657

1,1657

Now, list down the factors of 6870

1,2,3,5,6,10,15,30,229,458,687,1145,1374,2290,3435,6870

Greatest Common Factor

We found the factors 1657,6870 . The biggest common factor number is the GCF number.
So the greatest common factor 1657,6870 is 1.

Lets's calculate LCM of 584,824

Lowest Common Multiple of 584,824 using Common Division

2	584, 824
2	292, 412
2	146, 206
	73, 103

∴ So the LCM of the given numbers is 2 x 2 x 2 x 73 x 103 = 60152

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/60152

Therefore, the GCF of Fractions 1657/584,6870/824 is 1/60152

Least Common Multiple of 584,824 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 584,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(584,824) = 8

common factors(in case of two or more numbers have common factors) = 1

GCF(584,824) x common factors =8 x 1 = 8

LCM(584,824) = ( 584 × 824 ) / 8

LCM(584,824) = 481216 / 8

LCM(584,824) = 60152

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1657/584, 6870/824

1. What is the HCF of 1657,6870?

The HCF of 1657,6870 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 1657/584, 6870/824?

Answer: GCF of Numerators as per given numbers 1657/584, 6870/824 is

GCF of Numerators i.e. for 1657,6870 is 1

LCM of denominators i.e. for 584,824 is 60152.

Thus, GCF of Fractions is 1/60152.Finally, GCF of Fractions for 1657/584, 6870/824 is 1/60152.